How do I do this limit problem?

Question

I am trying to find the limit of (u+1)/(u^2-1) as u approaches 1. I had tried to factor "u+1" from the denominator. Afterword, I had tried canceling "u+1" from the denominator and numerator, but then I am only left with "u-1" in the numerator. So, I suppossed that the limit doesn't exist, but I must explain why this is so, if I am correct.

Answer 1

limit of (u+1)/(u^2-1) as u approaches 1

=limit of 1/(u-1) as u approaches 1

we can apply L'Hospital's Rule:

=Limit  of d/du  (1)/ d/du (u-1) as u approaches 1

=Limit 0/1  as u approaches 1

=0

 

Answer 2

Thank your help!